A place to write my way to understanding about issues related to teaching and learning. (Because of my experience, my focus is on mathematics education.) Please join me as I explore the changing educational landscape.

Saturday, August 27, 2011

The #mathchat topic for August 18th was "How do I get students to take the first steps in problem solving?" During the course of the chat, I asked the following:

Here are some of replies:

With the exception of @kassiaowedekind, very few details were provided. This is understandable given the limitations of Twitter, but I thought it might be worthwhile to continue the conversation using a venue that allows for more explanation. I will get us started with a couple of ways I have approached this question and then others can add their ideas in the comments.

The first approach I use is trying to avoid asking questions to which I already know the answer. I learned to do this while working with the first-graders in my wife's classroom. When I asked, "What is four plus three?" the first-graders typically responded with the expected answer and then waited for me to validate it. This was unrewarding to everyone involved. They were becoming reliant on me as the authority, and I really wasn't getting any insight into their thinking. Maybe they just knew the fact. Or they could have counted all, counted on, used doubles plus or minus one, or some other strategy. Or maybe they answered seven to every addition fact.

Instead, I decided to ask the first-graders, "How would you figure out four plus three?" Their answers to this were much more interesting to me. Although I had some ideas of how they might respond, I could not be sure and there were times I was surprised. Also, the first-graders always enjoyed sharing their thinking with me - much more so than just giving an answer.

The second approach is to share a problem I have not solved. I have some ideas of how to solve it but I have resisted the temptation to actually work on it. That way, when my learners ask if their solution is correct, I can honestly say, "I don't know." Then, they have to share their thinking, not just their answer, in order to convince me.

One of my favorite problems to ask the preservice teachers in my Teaching and Learning Middle Grades Mathematics course is, "When does 3/19 repeat?" We have tried graphing calculators and spreadsheet to no avail. As a result, we end up solving simpler problems looking for patterns and making conjectures. (I am told Wolfram Alpha can compute it but I refuse to spoil the fun - for now.)

Now it is your turn. Have you ever given a problem you didn't know the answer to? And if so, what was it and how did it go?

Thursday, August 18, 2011

I was catching up on watching some TED Talks this past week and found this one by Matt Cutts to be particularly appropriate for the start of a new school year.

The idea to try something new for 30 days is appealing to me as a teacher. It offers the opportunity to inventory my current practice and consider things I would like to add or subtract. I like the idea that the 30 day challenge represents an activity that encourages me to focus on the present moment. It reflects the ideas associated with the growth mindset and building trust in ourselves. Finally, the idea that the changes ought to represent small changes in order to be sustainable (what I call subtle shifts) really resonates with me.

Today, a group of middle school teachers came up with a list of things they want to work on this year to set the stage for continual improvement at their schools. This was the result of our discussion of chapter 8 from The Teaching Gap. Here is their list:

Volunteering more to be part of district teams developing exemplary lessons and assessments;

Engaging in more peer coaching;

Sticking to practices that are effective based on formative assessments even when standardized tests do not show immediate improvements; and

Spending more time reflecting on practice using a structured approach.

Given Matt's TED Talk, I suggested they consider focusing on these practices for 30 days in order to develop these as habits.

Wednesday, August 10, 2011

My vision of teaching and learning is summed up in my six-word teaching philosophy: engagement that fosters capacity and agency. This is based on my current understandings of the research of Vygotsky, Cambourne, and Johnston. It is also reflected in the National Resource Council's book How Students Learn. Putting structure to this vision has resulted in my implementation of the workshop model in the courses that I teach.

Planning and Instruction Portion of Teaching-Learning Cycle

I first read about this model for planning and instruction in Cambourne's book, The Whole Story. He saw it as a framework for providing the Conditions of Learning that he had identified in his research. Next, I became aware of a slightly different version of the workshop model used by various teachers from the Public Education and Business Coalition. Authors like Keene, Miller, and Conrad explained how this structure supports learners in developing the comprehension strategies they can use to make sense of the world. Nowadays, Lucy Calkins is a big name in Readers' and Writers' Workshop.

With my colleagues, Esther Billings and John Golden, we have modified these models to represent our theoretical framework of how to support learning. The specific structure is a combination of four key components that I have come to label connection, concentration, construction, and consolidation. We have also used schema activation, focus, activity, and reflection, but I like the alliteration.

Connection: The teachers or learners make connections between previous experiences and the present workshop. This provides a cognitive foundation on which to build new ideas. Schema activation was our original label because we liked the comprehension aspect - moving from the known to the new.

Concentration: The teacher sets the expectations for the workshop during this phase. By letting the learners know exactly what the focus is for the lesson, they are more likely to be engaged in the workshop because they know its purpose. Often, this looks like a mini-lesson based on the gradual release of responsibility that highlights the work the learners will be doing.

Construction: Learners are provided an opportunity to employ the idea presented during the concentration. This is the bulk of the workshop. An attempt is made to immerse the learners in authentic tasks so that they are learning in context and see the complexity surrounding the idea they are concentrating on. This usually includes some compulsory work, and perhaps a limited number of predetermined choice activities. While the learners work, the teacher is free to observe their progress, confer with individual learners, or provide a small group lesson.

Consolidation: This is the phase that attempts to ensure that learning lasts. It is imperative to provide learners with time to reflect on their experiences otherwise the response to "What did you learn today?" is a predictable "Nothing." We ask learners to look back at what they did and what it meant to them and to look forward to how their experience might transfer to other situations. This might entail writing (exit ticket), small-group sharing (round table), or whole class presentation (mathematician's chair). Typically, we use the formative assessment data collected during this phase to inform planning and build connections to future lessons.

In order to ensure that all phases are attended to, I often use an online stopwatch to manage our classroom time. This sometimes means interrupting learners during the construction phase before they are done, but usually they have engaged in enough of the activity to be able to reflect on it. When someone complains that they haven't finished, I respond, "Feel free to work more on it when you get some free time." Some take me up on this and some don't - it's their choice. I like to think that this builds what Ellin Keene calls, "learning lust."

I use the workshop format for in-class activities and for assignments. It even provides the framework for some of my assessments. Ultimately, the learners come to a point where they want less structure and more freedom. Then I turn the responsibility of designing workshops over to them. I provide the objective and the resources and they plan their time - keeping in mind that learning is supported by connections, concentration, construction, and consolidation.

Friday, August 5, 2011

The first cohort of W. K. Kellogg Foundation's Woodrow Wilson Michigan Teaching Fellow program descended on Grand Valley this summer. I have been teaching one of the many courses they have been taking in preparation for a year-long student teaching residency program beginning in the fall. My course, as the name states, is about facilitating learning environments. While I can offer them theories and my experiences teaching a middle school math class nearly two decades ago, I have relied on current K-12 teachers in my Professional Learning Network to fill in the gaps.

Already, the support has been amazing. Some of that support is chronicled here. Also, a few bloggers have posted their ideas about classroom management (here and here) and included the course hashtag, #FLE11, in their tweets so that the Fellows would have access to their experience and wisdom.

You all have given so much already but I have another request. As a part of a home workshop, Fellows were asked to come up with a list of questions they had about facilitating learning environments. They have posted these on their blogs. I would appreciate it if you would take some time to read these posts and provide answers to their questions when possible.

About Me

I am a professor in the Mathematics Department at Grand Valley State University. Mostly, I teach future teachers but I also do some professional development with inservice middle school teachers. My six-word teaching philosophy is: "Agency and capacity fostering sustainable learning."
My wife, Kathy, is a first grade teacher. She is the person who keeps me grounded in educational reality when I begin to get too idealistic. I have also learned a great deal from her about comprehension strategies and instructional coaching.
I have three adult step-children (Hilary, John, and Andrew).